Or what is the use of a black cover instead of a silver one?
I have the idea that the black (only) removable cover of some umbrellas is rather an incomplete product. Is that so?
I'll try to elaborate.
A simple umbrella can be used as a reflector or as a translucent diffuser. If you need the diffuser, you remove any cover. That one is clear.
But if you need it as a reflector to bounce light, you have three options: 1) Leave the cover off 2) Use a black cover 3) Use a silver cover.
Considering that the umbrella is translucent, if you go for option 1, part of the light goes to the other side. If you are in a small room it means that some of the light will then bounce off the wall and come back to the subject. If you are outdoors or in a really big hall, there is nothing to bounce the light back so it is just lost (wasted light).
Using a cover, either black or silver will prevent light going through the umbrella. In a room it means less light hitting the walls and coming back to the subject in many directions, eliminating some "fill light" and giving a more contrasty look. But outdoors the cover won't provide that benefit.
There is where my struggle begins. My guess is that a silver cover shall bounce the light back into the umbrella, which should cause it to go through the fabric one more time and then directly to the subject, thus making a better use of the light source, while a black one will simply eat the light up. That would make the silver cover a much better choice, specially if using small flashes and shooting outdoors.
So, again, is there a reason why someone would prefer to buy an umbrella with black covers instead of the silver one?